The theme is using fa icons. But if you select an icon for the pages then the bootstrap images are used and the font awesome icons are lost. How can I enable font-awesome so that these icons can be selected too? I now succeeded by modifying the database directly, but...

Yes, that black window (icon manager) - there are more icon sets together. And you don't know what icon belongs to what set. You can see it in source code on your frontend (if there is code glyph, you select wrong icon in admin). In fact from your frontend code I will able to find problem - if there is missing "fa" before icon name, theme needs update to latest core changes.

Well, actually when I use the free icon names fa_etc. in the database it works well. The problem is that I have difficulties selecting the right icons then from the icon panel if I can't see if it's a fa_ or the 'old ones'. The theme comes in two flavours, B3 and B4. Afaik E107 is still B3 so I choose the B3 variant. But that one appears to use fa_ icons, which - on itself - is not too bad. The only problem is that you cannot select them from the admin panel (I thought). But if they are mixed with the others... Then it's a puzzle. You don't see the physical names...